Dissipation compensated phase shift network



Aug- 23, 1955 WOLJA SARAGA 2,716,220

DISSIPATION COMPENSATED PHASE SHIFT NETWORK Filed Nov. 27, 1953 4Sheets-Sheet l RR2 AND IVO/V21 As 1N FIGA R R2 AND IVO/V2] AS 1N FIG. 4

H50 5., HE., 6.

.4N-mensys,

Aug. 23, 1955 woLJA sARAGA 2,716,220

DISSIPATION COMPENSATED PHASE SHIFT NETWORK Filed Nov. 27, 1953 4Sheets-Sheet 3 0 o .o ourpur o l All 4 Trae/v5 v5.

Aug- 23, 1955 woLJA SARAGA 2,716,220

DISSIPATIONCOMPENSATED PHASE SHIFT NETWORK Filed Nov. 27, 1953 4Sheets-Sheet 4 Hi @L R GX ED 2/ o mi: ETwoRKl NETwoRKZ /7 ale/Veys.

2,7l,229 Patented Aug. 23 1.9.55

DISSIPATION COMPENSATED PHASE SHIFT NETWORK Wolja Saraga, Orpington,England, assgnorto Telephone Vlvlanufacturing Company Limited, a Britishcompany Application November 27, 1953, Serial N 394,825

Claims priority, application Great Britain February 16, 1953 4 Claims.(Cl. 3.33-29) 'This invention relates to electrical impedance networksof the type producing a constant loss and a varying phase shift withvarying frequency.

It would be possible at least in theory, to design networks having thisproperty, if ideal reactive elements having no resistive or .dissipativecomponents were available. Such idealized networks are impossible ofconstruction, however, since ideal reactances free from resistivecomponents do ,not exist.

Objects of the present invention are to provide dissipation-compensatedphase shift networks which produce a constant -loss and a phase shiftwhich varies with frequency, thus simulating an idealized `phase shiftnetwork although the constant loss is somewhathigherthan would be thecase for a corresponding phase shift inetwork without dissipation.

This and other objects and the advantages of the in- Vvention Iwill beapparent from the lfollowing -specication when taken with `theaccompanying drawings in which:

Figs. 1 to 6 are diagrams of idealizedphase shift networks in `which thereactances are ideal 4reactances free from resistive components; yandacross the output termination 'is V2 then the modulus of the voltagetransfer ratio Vo/2V2) is and the attenuation 1in vdecibels ,is

It is possible to alter one of theseresistance Ro without altering thephase shift; then a basic at loss occurs, that is, .the attentuation isincreased luniformly through the frequency range by a given amount inthe manner indicated Vin Figure 2. In Figure 2, the two resistances Roareshown as replaced byresistances R1 and R2 respectively.

With this network, if R1:Ru and R2:v1Ro, where -17 Ais an arbitraryconstant, then the modulus of the voltage transfer ratio is Ygiven by Vni( l) 2V2-V2 1+i; Alternatively if R2=Ro 'and cuits which are wellknown.

2 then Equation 1 still holds. These relations ,are shown in the legendto Figure 2. It will -be seen'that for 17:1, i. e. for thecase shown inFigure 1, Equation .l becomes V0 2V2 i. e., the correct relation 'forFigure 1.

It is possible to replace the two lattice arm reactances by resistancesRo withoutaltering the phase shift, lin `the manner indicated in ,Figure3. Then, .if the soureeand 'load resistance are both equal to R0 a flatloss of 6 db is lproduced as compared with the circuit .of Figure 1. Itis possible to make the source resistance V1 iR" and the load resistanceRe when an addition at loss depending on a7 is produced, rwithout`altering the phase shift characteristic, The modulus of the voltagetransfer ratio Vo/2V2 is then given by the relation:

l 2 n :it 2V2 211 it will -beseen thatfor 11:1 -Equation 2 'becomesThus, if 1;:1 the basic loss is 12 db instead of 6,-db.

Two other types of phase shift networks, shown restively in Figures 5and 6 can be shown to Ybe special cases of the network of Figure 4 butwith more reactive elements than are necessary for producing the phaseshift actually produced. The -circuit in Figure 4 can be .replaced .invknown manner by a hybrid circuit or by one of a Ynumber of so-calledhalf-lattice networks which are driven from a Abalanced source. lForinstance, half lattice networks have been described .by R. B. Dome,Electronics, December 1946, p. 1'12 et seq., in an article entitled Wideband phase Vshift networks, by'D. G. C. Luck, Proc. I. R. E., vol. 37,Pt. ll, 1949, p. 147 et seq., in an article entitled Properties of somewide band phase splitting networksfan'cl by the present applicant inBritish Patent No. 653,696.

The principal advantage of half ,lattice networks in respect to thepresent invention is that, being electrical alternatives to the networkshown in Figure 4, they employ a single resistive arm with impedance jXas shown in Figure 4a. The two .phase input voltage, i. e., two voltagesof equal amplitude but opposite phase, `required by such networks may bederived by one of the circuits shown in Figure 4b or 4c and referencemay also be made tothe previously quoted British Patent No. 653,696and'vto Figures 13 `and 14 of an article entitled An aerial analoguecomputer, yby W. Saraga, D. T. Hadleyiand F. Moss appearing in the Jnl.Brit. I. R. E., vol. '13, No. y4, p. 201 et seq., April 1953.

A hybrid circuit equivalent to the network shown in Figure 4 isillustrated in Figure 4d but it will be realised that this is only oneof ymany such equivalent hybrid cir- Reference may also be o made toFigure 4 of British Patent No. 653,696 previously quoted. In the circuitshown in Figure 4d, ZA and 1/zZA are the impedances of the threewindings of the transformer.

In the networks of the invention, the ideal reactances of the idealphase shift networks, such as those of Figures l to 5, are replaced byarms consisting of dissipative reactances and additional resistances,and the nature of these arms will be more particularly describedhereinafter. Before proceeding to this description, however, it isconvenient to point out a generalisation of ideal phase shift networks.

The phase shift networks described above and shown yin Figures l to 5are completely determined by the impedance of one of the reactive armsof the network. For example, in Figures l to 5, all the networks aredetermined by the impedance jX, and this impedance, identified as Z willbe called the characteristic impedance of the network. In the idealnetworks of Figures 1 to 5, the impedance Z is purely reactive, namelyZ=jX. The impedances of the other reactive arms are equal to jX, or tothe inverse form Rs2/Z that is, 1R02/X where Ro is a constant resistancevalue, which within certain limits-taking the values of the sourceresistance and load resistance into account-can be given an arbitraryvalue. The resistive arms of the networks are then Ro.

It should be appreciated that, in any of the phase shift circuits underdiscussion, replacing the impedance iX by its inverse form Ro2/jX andvice versa results only in a phase reversal i. e. a constant phase shiftof 180. This constant phasey shift "is of no practical significance asit can be eliminated by a conventional reversal of terminals, thus anyof the circuits shown are equivalent to a circuit derived from theexample by replacing all impedances X by Roz/iX and vice versa. Thistruth also applied to circuits shown with a single reactive impedancesuch as Figures 4, 4a and 4d.

As Z determines the phase shift network completely,

- the phase shift produced by the network can be expressed in terms ofZ=X only. The transfer constant 0=oc+i of the phase shift network, wherea has the dimension of a loss innepe'rs but is zero as long as Z ispurely reactive and ,8 is the phase shift in radians, is given by therelation when 0::'0 and Z=jX for the case of zero dissipation.

Dissipation occurring in the reactive elements of a phase shift networkwhich has been designed under the assumption of zero dissipationproduces in general two undesirable effects; the loss a is no longerconstant but varies with frequency, and the phase shift actuallyproduced by the dissipative reactance X differs from the phase shiftwhich would be obtained with the same reactance X without dissipation.

In Vcarrying out the present invention there are three considerationswhich apply. In the first place it is well known that any phase shift/frequency curve which can V,be produced by a passive network can beproduced by a number of elementary phase shift networks in tandem,

where ank elementary network is a network with the characteristicimpedance iRnax in the case of a oneparameter network or a network withthe characteristic impedance jRoax/ (1-6x2) in the case of atwo-parameter network, where x is the normalised frequency /ref, fretbeing an arbitrary reference frequency and a, a, b are suitably chosenreal parameters. Thus the first impedance is that of an inductance,while the second that of a parallel tuned circuit. It is thereforesufficient to provide` dissipation-compensated versions of one-parameterand twoparameter phase shift networks, the problem of providing a morecomplex phase shift network with `dissipation lcompensation beingsolvable by connecting a number of 4 I Y, such elementary dissipationcompensated networks in tandem.

In the second place, the incidence of dissipation will necessarilyincrease the basic loss, but it is possible to make the loss constant inspite of the presence of dissipation if resistances are added to thedissipative reactances in such a way as to make the characteristicimpedance to be of the form lJ-rJ'X/Ro ao-l-j Z-R01+7.CX/RD-R tanh 2 (6)Where X is of the form of a physically possible ideal reactance withoutdissipation and 010:2 tanh"1C is a constant loss (in nepers) independentof frequency.

The third consideration is that of the modification of the phase-shiftfrequency curve. So far, reference has been made to compensation for oneeffect of dissipation only, namely the occurrence of a loss varying withfrequency. It will be shown'that the second effect, the modification ofthe phase-shift/frequency curve, can be compensated for by modifying theideal reactance function in accordance with some relation to bedetermined, taking into account the amount of dissipation to beexpected.

In this way the problem reduces to designing two types of network, onesuitable for replacing ideal one-parameter reactances having animpedance of the form Z/Rozy'ax, or in the case of the inverse form,Ro/Z=jax whilst the other is suitable to replace an ideal two-parameternetwork having an impedance of the form or in the case of the inverseform Ro/Z=jax/(lbx2). In both cases the substitute networks must have aphase shift the same as that of the network it replaces and a at loss.

It is convenient to express the desired phase shift B in terms of theseparameters a, a and x. Thus in the case of the one-parameter networkz=R0j71x and from Equation 6 above Hence ,8:2 tan lax (7) With thetwo-parameter network Since 0:0 with the ideal network, we have ,3:2tan-1 (s) In the substitute networks. it will be assumed that thenumerical value of the dissipation of all reactive elements is the same.Though this does not normally occur in practice since the dissipation ofinductors is generally and, as before,

whence 5 higher than that of capacitors, the condition can be met Forthe one-parameter ideal networkZ/Ri=jx, cto-:0.

vTheisubstitute network must have impedance Z such that ,`Z/Ro or Ro/Z,as the case may be, is equal to where C=tanh fr0/2, a0 `being the basicloss of the network. It can be vshown that in the case of an inductanceas shown in Figure 8(a) a substitute network consisting of aparallelcombination of a resistance and a series combination -of a ,pureinductance and a resistance as shown in Figure 8(b), can be given valuessuch as to provide an impedance .of the desired form. If the firstresistance has the value, normalised with respect to Ra of e, the secondresistance the .normalisedzvalue c/Q and the inductance the AnormalisedVimpedance Vvalue jcx, yas indicated in Figure 8(b), then the desiredimpedance is obtained .if

and e=Q/a (-9) kmr@ where Q Vis the reciprocal of the ,dissipationconstant. 'The elements of the network will be positive if Q is not ,too

Z jaa: 1 bz2 l 0) and the phase shift is ,9:0 tan-1 ggz (il) Itis .thusnecessary to nd an impedance Z as stated above, so that Figures 9(b) and9(0) show the required vdissipative networks. Figure9(b) shows a seriescombination of a normalized resistance Vl: and aparallel combination ofa normalised impedance Zi/Ru and a normalised im- .pedanceDRo/Z1, Dbeing a constant dened hereinafter, -It1will be apparent that it' a.network with 'normalised vimpedance Zl/'Ru is given, the network ofnormalised impedance DRo/ Z1 is also determined as-it-isthe networkinverse to the rst with respect to resistance Rim/D.

Thus, only the network Zi/Ro need be determined.

The limpedance Zi/Ro takes the form, shown in Figure 9, of a parallelcombination of a resistance of normalised value e and a seriescombination of a'normalised resistance of value c/ Q and an inductancewith normalised impedance jcx the values being defined by the followingrelations:

GUI-QW lll 6 Withlthis network the basic loss is Vgivenlby 4b@ -l E. an2 tanh a b+Q2) `Figure 9(c) shows the second network which can .besubstituted .for the two-,parameter .dissipative networks. It consistsof a parallel combination of an impedance Zi/Ro, a normalised`resistance F and an impedance DRU/Z1. In this case the impedance Zl/Rotakes the same form, lshown 'in Figure 9, as for the network of Figure9(b) andrelations (13), (14), and (l5) apply. yIn place of Equations '16and 17, the following holds:

A=to+Q2 2a2Q2JQ (18) (QZ-W F`(a2-4b b+Q2 Q (19) With this network thebasic loss is given by:

Y0:2 mnh-14 53322) (2 0) As explained above Q is the normal reciprocalof ,the dissipation constant and for an inductance L with effectiveseries resistance RL is given by .and for .a .capacitance C with shuntresistance Rc -is given .by

Q =21rfrefCRC in lFigure 9(c) it is, ofcourse, possible to absorb thenormalised resistance F in Zi/Ro. It will be seen that F is negative linFigure 9(b) if a2 4b and negative in Figure 9(6) if a2 4b. In Figure9(0) F 0 does not make the network necessarily non-physical.

.if 122% -the vphase shift network `defined by the series .arm.reactance in Figure 9(.a.) can be replaced Yby 'two `simpler networks,in ytandem of `the type defined by the series Aimpedance in Figure8(11).

x'One Vuse "of `a dissipation 'compensated network -in accordance withthe invention is in phase splitting net works of the type described inapplication Ser. No. 169,303, now rPatent No. 2,661,458, of which this.applivcation lis va I,continuation-impart application.

I claim:

l. An elementary phase shift dissipation-compensated network forproducing over anextended frequency range a constant loss and a phaseshift l in radians defined :by ,the relation:

the reactances of the ideal network which are positive having animpedance Z2 defined by the relations:

where Ru is an arbitrary and constant value of resistance and thereact-ances of the ideal network which are nega- 'tive have the inverseform of the positive'reactances 'and yare of value Rs2/Z2, the saiddissipation-compensated network comprising in the position of areactance of the ideal network a substitution impedance having animfpedauce `Z1 which is dened'by the lrelation 756:(DL1`a2) where al'isVthe loss, vin nepers, of the dissipation-'compensated network anda.,that of the said corresponding ideal network, said substitutionimpedance consisting of the parallel combination of a rst branchconsisting of resistive component of value QRo/, with a second branchconsisting of a reactive component of value jRocx and and Q is the ratioof the reactance to resistance of the 1 respective components of thesaid rst branch at the normalized frequency x=l, and comprising in theposition of a reactance of the ideal network which is of the inverseform, animpedance which is of inverse form, with respect to Ro, of saidsubstitution impedance.

2. An elementary phase shift network in which the effect of thedissipative component inherent in the impedance of the nominallyreactive elements is counteracted by the effect of additional purelydissipative elements introduced into the network to provide adissipation compensated network which produces a constant loss a, innepers, over an extended frequency range and a phase shift l, inradians, defined by the relation 51:2 tan-1 Ex where a is a real andpositive constant and x is the normalized frequency f/fo, f being thefrequency at which the phase shift is determined and fn an arbitraryreference frequency, said network corresponding to an ideal elementaryphase shift network, ideal in the sense that ity employs only reactiveelements which have no inherent dissipative component, said reactiveelements which are positive having an impedance Z2 such that and thosewhich are negative having an impedance Roz/Z2, where Rn is an arbitraryand constant value of resistance, said ideal network producing aconstant loss a, which may be zero, in nepers, over an extendedfrequency range and a phase shift A9 in radians, such that [31:18,:2tan*1 'Ex Vand in which. said positive reactive elements correspond tocircuit elements in the dissipation-compensated network having animpedance Z1: R0 mnh ily@ where a0=a1a2 and comprising a parallelcombination of a purely dissipative element of value QRu/a and adissipative positive reactive element represented by a seriescombination of a non-dissipative positive reactance of impedance valuejRnCx and a purely dissipative cornponent of impedance value CRo Q whereby the relation ax 1--bcv2 where x is,the normalized frequency,expressed as. the

,B1 2 tall-1 i3 ratio x=f/f0, where f is the frequency and fu is anarbitrary reference frequency and -a and b are real and positiveconstants, and for producing substantially constant loss over anextended frequency range, said network corresponding to an idealelementary phase shift network the reactances of which aredissipation-free and which produces a constant loss, which may be zero,and a phase shift defined by the relation z 2 tan (1 bx2 in which thedissipation-'free reactances of the ideal network are replaced bysubstitution impedances, said substitution impedanceshaving acharacteristic impedance Z defined by the relationv where R0 is anarbitrary and constant value of resistance, a., is difference, innepers, between the loss ofthe dissipation compensated network and thatof the said corresponding ideal network, said substitution impedancecomprising in the position in the ideal network of an ideal parallelresonant circuit of normalized impedanceV a resistance, of normalizedvalue F, in series with a parallel combination of two impedances Zi/Roand DRn/Z1, where Z1/Ro is a parallel combination of a rst branchconsisting of a series combination of a resistive component ofnormalized value c/Q and an inductive impedance component of value jcx,and a second branch consisting of a resistive component of normalizedvalue e all as defined by the relations: t

4. An elementary dissipation-compensated phase shift network forproducing a phase shift1 in radians defined by the relation -x i l tall1 bmg) where x is the normalized frequency, expressed as the ratiox=/;fn, where f is the frequency and fo is an arbitrary referencefrequency, and a and b are real and positive constants,` and forproducing substantially constant loss over an extended frequency range,said network corresponding to an ideal elementary phase shift networkthe reactances of which are dissipation-free and which produces aconstant loss, which may be zero, and a phase shift defined by therelation in which the dissipation-free reactances of the ideal networkare replaced by substitution impedances, said substitution impedanceshaving a characteristic impedance Z defined by the relation where Re isan arbitrary and constant value of resistance, a, is difference, innepers, between Vthe loss of the dissipation compensated network andthat of the said corre- 9 spondng ideal network, said substitutionimpedances comprising in the position, in the ideal network of an idealparallel resonant circuit of normalized impedance a resistance, ofnormalized value F, in parallel with an impedance of value Zi/Ro and animpedance of value DRn/Z1, where the impedance of value Zi/Ro is aparallel combination of a first branch comprising a resistive componentof normalized value c/Q in series with an inductive component ofnormalized value jcx and a second branch consisting of a resistance ofnormalized value e all as dened by the relations and Q is the ratio ofreactance to resistance of the respective components of the said firstbranch, and in which the inverse forms of the ideal elementary phaseshift network are replaced by the inverse forms of said substitutionimpedances.

References Cited in the tile of this patent UNITED STATES PATENTS2,228,869 Chireix Jan. 14, 1941

